Надо, . доказать тождество: (cos4x+1)/(ctgx-tgx)=1/2sin4x

Sin2x=2sinxcosx
cos(4x)+1=2cos^2 (2x) -1+1=2cos^2 2(x)
ctg (x)- tg (x)= cos(x)/sin(x)-sin(x)/cos(x)=(cos^2 (x)- sin^2(x)) / sin(x)cos(x) = cos(2x)/sin(x)cos(x)
2cos^2 (2x) : cos(2x)/sin(x)cos(x)= 2cos^2(2x)*sin(x)cos(x)/cos(2x)=2cos(2x)sin(x)cos(x)=cos(2x)sin(2x)=1/2*sin(4x)